Modified Chebyshev algorithm: some applications

Two applications of the modified Chebyshev algorithm are considered. The first application deals with the generation of orthogonal polynomials associated with a weight function having singularities on or near the end points of the interval of orthogonality. The other application involves the generation of real Szego polynomials.

Studies on the constituents of a Brazilian folk infusion. Isolation and structure elucidation of new triterpene saponins from Ilex amara leaves

The isolation of three new triterpene saponins 3beta-O-beta-D-glucopyranosyl-(1-->3)-alpha-L-2-O-acetylara-binopyranosylolean-12-en-28-oic acid 28-O-beta-D-glucopyranosyl ester (2), 3beta-O-beta-D-glucopyranosyl-(1-->2)-alpha-L-O-arabinopyranosylurs-12-en-28-oic acid (3), and 3beta-O-beta-D-glucopyranosyl-(1-->2)-beta-D-O-galactopyranosylurs-12-en-28-oic acid (4) together with five known saponins and one flavonoid glycoside from the aqueous infusion of flex amara (Vellozo) Loes. leaves is reported. All structures were elucidated by spectroscopic methods, including the concerted application of one-dimensional (H-1, TOCSY, C-13, and C-13 DEPT NMR) and two-dimensional NMR techniques (DQF-COSY, HSQC, and HMBC).

Antiplasmodial activity of aryltetralone lignans from Holostylis reniformis

Extracts from Holostylis reniformis were tested in vivo against Plasmodium berghei and in vitro against a chloroquine-resistant strain of Plasmodium falciparum. The hexane extract of the roots was the most active, causing 67% reduction of parasitemia in vivo. From this extract, six lignans, including a new (7 ' R,8S,8 ' S)-3 ',4 '-methylenedioxy-4,5-dimethoxy-2,7 '-cyclolignan-7-one, were isolated and tested in vitro against P. falciparum. The three most active lignans showed 50% inhibitor concentrations of <= 0.32 mu M. An evaluation of minimum lethal dose (30%) values showed low toxicity for these lignans in a hepatic cell line (Hep G2A16). Therefore, these compounds are potential candidates for the development of antimalarial drugs.

Caries resistance of lased human enamel with Er : YAG laser - morphological and ratio Ca/P analysis

Objective: In vitro analysis of caries resistance of dental enamel under caries simulation after irradiation with Er:YAG laser. Background Data: More susceptible to caries development spots at adjacent hard tissues from cavity preparations of dental tissues using burrs or lasers are quite common. Methods: Thirteen caries-free third permanent human molars were distributed as follows: G1: sound control and caries control; G2: Er:YAG 100, 200, 300, or 400 mJ/ 10 Hz/ 3 sec.; G3: the same parameters of G2 followed by artificial caries simulation, through dynamic model of demineralization and remineralization (DE/RE). Caries resistance analysis was evaluated through scanning electron microscopy (SEM) and Ca/P rate (X-Rays spectroscopy - EDX). Results: Photomicrographs showed that the Er:YAG laser created craters with rough aspect which became more evident as the energy per pulse was increased, but without change of regular morphology of enamel prisms. Significant statistical changes among the irradiated and control groups was observed considering the Ca/P ratio. Conclusion: Irradiated groups showed higher caries resistance than control groups. However, it is not possible to affirm that the enamel surface accidental irradiation could be a benefit to caries resistance for other situations can be considered, as biofilm deposit, which could increase the caries susceptibility.

Chebyshev-Laurent polynomials and weighted approximation

Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.

Enamel caries resistance accidentally irradiated by the Nd : YAG laser

When the carious tissue is eliminated either by conventional methods (with burs) or with lasers, the risk of accidentally damage the surface of adjacent teeth may occur, which hypothetically could lead to a more susceptible surface for canes formation. This in vitro study aims to evaluate the caries resistance of the dental enamel surface irradiated by the Nd:YAG laser applied in conditions simulating accidental exposition. Thirteen third molars were used in this study. The experimental groups were: G1: sound control and control + carious; G2: contact Nd:YAG laser at 0.75, 1, 2, or 3 W; 10 Hz; 3 sec (27, 35, 71, and 106 J/cm(2)); G3: same parameters from G2 + caries artificial induction through the demineralization and demineralization (DES/RE) dynamic model. The caries resistance analysis was evaluated by the superficial morphological aspect through SEM images and also by Ca/P proportion through energy dispersive X-ray spectroscopy (EDX). The micrograph images showed that the Nd:YAG laser changed the normalmorphology of the enamel prisms resulting in a melted and re-solidified surface intensified with the power increase. Significant statistical differences were observed applying the Kruskal-Wallis statistical test (p <= 0.01) among the Nd:YAG laser irradiated groups and the control with caries regarding the Ca/P proportion. As an exception, this was not observed when 3 W; 10 Hz; 3 sec; 106 J/cm(2) was applied and posteriously submitted to a cariogenic challenge. The results indicate that the Nd:YAG laser accidental irradiation at low power settings did not represent risks to the enamel caries resistance.

Morphological and anatomical observations about Mariliasuchus amarali and Notosuchus terrestris (Mesoeucrocodylia) and their relationships with other South American notosuchians.

The phylogenetic relationship of the notosuchians Mariliasuchus amarali (Campanian; Bauru Group) and Notosuchus terrestris (Santonian; Neuquen Group) is revised. Morpho-anatomical evaluation of Mariliasuchus in the current bibliography indicate close relationship with Notosuchus, while cladistic analysis either related Mariliasuchus to Candidodon itapecuruense (Albian/eo-Cenomanian; Sao Luis-Grajau Basin), as part of the phylotaxon Candidodontidae, or to Comahuesuchus brachybuccalis (Santonian; Neuquen Group). Comparative study of specimens shows similarities on the palate, choanae, dentition, retroarticular process, and other structures from Mariliasuchus and Notosuchus supporting the original classification as a Notosuchidae. Preliminary phylogenetic analysis sets these taxa as sister-groups. Reevaluation of a previously published phylogenetic analysis from other authors provides further support for the Mariliasuchus + Notosuchus clade. The current work indicates that Mariliasuchus is a Notosuchidae, refuting its allocation as a Candidodontidae. The influence of character construction and the definition of Notosuchia are discussed.

Morphology of the dental carinae in Mariliasuchus amarali (Crocodylomorpha, Notosuchia) and the pattern of tooth serration among basal Mesoeucrocodylia.

Carinated teeth are common in Mesoeucrocodylia, and the occurrence of denticles over the carinae is related to high predacious species, often referred as ziphodont. This characteristic is broadly recognized as homoplastic. Carinae morphology is cryptic, difficult to be studied under common techniques, and Scanning Electronic Microscopy (SEM) allows the access to detailed information, offering a higher degree of confidence. Previous SEM study allowed the recognition of true/false ziphodont patterns, according to the morphology of the denticles, but such studies on gondwanan mesoeucrocodyles are uncommon. Mariliasuchus amarali is an Upper Cretaceous notosuchian mesoeucrocodyle from South America (Bauru Group, Brazil), with carinated teeth and specialized dentition. Its geological and biochronological distribution are reappraised. SEM study of two teeth shows carinae composed of isolated tuberous anisomorphic true denticles, supporting previous study. Enamel ornamentation does not develop over the carinae, and fabric becomes anastomosed in middle and posterior teeth. Carinae only occur in posterior molariform teeth, related to food processing. Morphological variability of Mariliasuchus is commented, focusing on dentition. Overall characteristics, molariform morphology and wear planes support a non-predacious habit for Matiliasuchus. Matiliasuchus pattern could not be related to true/false ziphodont patterns, either by morphology or function, and is defined as ziphomorph. Ziphomorph pattern is evaluated within the range of mesoeucrocodyles. The detailed study of homoplastic characteristics, such as dental carinae, may provide useful apomorphic information for cladistic analysis.

Sequential spectrophotometric determination of chromium(III) and chromium(VI) using flow injection analysis

A flow injection analysis (FIA) procedure for the speciation of Cr(III) and Cr(VI) using the 1,5-diphenylcarbazide (DPC) method is presented. As Cr(III) does not interfere in the Cr(VI) - DPC reaction, both Cr(VI) and total chromium [after the on-line oxidation of Cr(III) by Ce(IV)] are sequentially determined. Cr(III) is obtained by difference. Under the experimental conditions described, the calibration graphs are linear up to 2 μg mh1 of Cr(VI) and 4 μg ml-1 of Cr(III). The detection limits found were 18 ng ml -1 for Cr(VI) and 55 ng ml-1 for Cr(III), at a signal to noise ratio of 3. The common interfering elements in the Cr(VI) - DPC reaction were investigated under dynamic FIA conditions. The FIA method was also compared with the conventional spectrophotometric procedure.

Gravitational Lorentz force and the description of the gravitational interaction

In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analogue of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the Riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of general relativity. The main conclusion is that scalar matter is able to feel any one of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.

Riemannian and teleparallel descriptions of the scalar field gravitational interaction

A comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field. In contrast to the current belief that only spin matter could detect the teleparallel geometry, scalar matter being able to feel the metric geometry only, we show that a scalar field is able not only to feel anyone of these geometries, but also to produce torsion. Furthermore, both descriptions are found to be completely equivalent, which means that in fact, besides coupling to curvature, a scalar field couples also to torsion.